Hammond said: “Our thoughts are with the family and friends of Steven Sotloff.

“We are doing everything we can to reassure the family of the British hostage who was shown in the video.”

He also suggested the Government could launch a fresh rescue attempt, adding: “We will look at every possible option to protect this person.”

Security minister Admiral Lord West, the former head of the Navy, said US Special Forces would go after the killer in the same way they executed Osama bin Laden.

James Foley, an American journalist, was beheaded by IS terrorists.

Lord West said: “We probably know already who he is, we certainly will know soon. He is a dead man walking, and he wants to think about that.”

At Prime Minister’s questions yesterday, David Cameron told MPs: “All our thoughts are with the British hostage and his family. Their ordeal is unimaginable.

“This country will never give into terrorism. Our opposition to Islamic State will continue at home and abroad.

“A country like ours will not be cowed by these barbaric killers. If they think we will weaken in the face of their threats they could not be more wrong.”

Labour added: “Events like this must strengthen not weaken our resolve to defeat them.”

Hammond said the hostage situation would not alter the Government’s stance on dealing with Islamic State.

He said: “It can’t allow us to change our overall strategy.

“We’ve been aware of this hostage, of course, for some time, but we have to deal with Islamic State on the basis of the wider threat that they pose to the British public, as well as to this individual.”

And he added: “It doesn’t make any difference at all to our strategic planning.

“As the Prime Minister said, we will look very carefully at the options available to us to support the legitimate government of Iraq and Kurdistan in defending themselves from the threat of Islamic State.

“And if we judge that airstrikes could be beneficial, could be the best way to do that then we will certainly consider them, but we’ve made no decision to do so at the moment.”

Barack Obama said that the US will not be intimidated by Islamic State and will build a coalition to “degrade and destroy” the group.

The president vowed the US would not forget the “terrible crime” against Sotloff and Foley.

He said: “Our reach is long and justice will be served.

“Our objective is to make sure that Islamic State is not an ongoing threat to the region. And we can accomplish that. It’s going to take some time and it’s going to take some effort.”